Despite its recognition as a lifesaving intervention and cornerstone of modern intensive and emergency care, mechanical ventilation can be both uncomfortable and injurious. Complex interactions between patient characteristics and the manner in which the ventilator applies flow and pressure determine the level and adequacy of support, the degree of patient comfort, and the potential for injury. Patient: ventilator interaction is a complex and dynamic process, fraught with feedback loops and adaptation. This complexity is of greatest importance in the setting of pressure support noninvasive ventilation (PSNIV), an increasingly common approach to supporting individuals with respiratory failure. There is not at present a rigorous conceptual foundation for optimizing the application of PSNIV. We will develop both a mathematically rigorous conceptual framework and a suite of practical tools for analyzing, monitoring, and optimizing the application of pressure support noninvasive ventilation by accomplishing 4 specific aims. 1) Specific Aim One: Develop, calibrate, and validate practical mathematical models and tools for the real- time analysis of pressure support noninvasive ventilation; 2) Specific Aim Two: Use human data to construct libraries of patient impedance (lung "stiffness" and resistance) characteristics and patterns of respiratory effort during assisted breathing and systematically investigate interactions between model complexity and the accuracy and robustness of model predictions; 3) Specific Aim Three: Apply contemporary mathematical techniques to identify approaches for applying PSNIV that are anticipated to improve the likelihood of adequate support in specific populations; 4) Specific Aim Four: Develop automated, noninvasive tools to a) identify airway opening flow- and pressure profiles indicating potential patient: ventilator conflict and b) objectively classify patient breathing patterns. These tools will be developed from "first principles," with rigorous mathematical and laboratory analyses and optimization that will be tightly linked to clinical calibration, evaluation, and validation. This work will ultimately help us to better manage patients who are treated with noninvasive ventilation, whether for an acute illness (such as an exacerbation of emphysema), or at home (as in the case of obstructive sleep apnea).